Cremona's table of elliptic curves

1025 = 5² · 41

Field	Data	Notes
Atkin-Lehner	5+ 41+	Signs for the Atkin-Lehner involutions
Class	1025a	Isogeny class
Conductor	1025	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	131328125 = 57 · 412	Discriminant
Eigenvalues	-1 -2 5+ -2  0  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-688,6867]	[a1,a2,a3,a4,a6]
Generators	[17:4:1]	Generators of the group modulo torsion
j	2305199161/8405	j-invariant
L	1.1302450721524	L(r)(E,1)/r!
Ω	1.8577562515014	Real period
R	0.30419627742848	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16400n2 65600e2 9225x2 205c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1025a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	-2	+	-2	0	4	-4	0	8	2	0	6	+	-8	-2	-8	-12	2	-10	8	6	-8	-12	14	8

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Quadratic twists for elliptic curve 1025a2

-4	8	-3	5	-7	-11	41
16400n2	65600e2	9225x2	205c2	50225l2	124025j2	42025c2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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